$A$ $B$ $C$ If: $ AC = 26$, $ BC = 7x + 2$, and $ AB = 9x + 8$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 8} + {7x + 2} = {26}$ Combine like terms: $ 16x + 10 = {26}$ Subtract $10$ from both sides: $ 16x = 16$ Divide both sides by $16$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 7({1}) + 2$ Simplify: $ {BC = 7 + 2}$ Simplify to find ${BC}$ : $ {BC = 9}$